Modelagem econométrica dos principais indicadores econômicos do Brasil: pré e pós a crise financeira mundial de 2008
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2023-12-05
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Universidade Estadual Paulista (Unesp)
Resumo
A crise financeira mundial de 2008 foi a maior crise desde 1929, vários países do mundo sentiram seu impacto e entre eles está o Brasil. Uma forma de medir esse impacto na economia é através de alguns indicadores econômicos, e esse trabalho tem como objetivo utilizar técnicas estatísticas para modelar alguns desses indicadores como o IPCA (Índice de Preço ao Consumidor Amplo), Preços das Exportações e Importações e as Taxas de Juros e de Câmbio. Para as análises foram coletados valores mensais dos anos de 2006 a 2009, foram aplicados os modelos de regressão de decomposição temporal e de regressão harmônico (senos e cossenos) junto com variáveis “dummy” Para verificar se houve diferença entre os períodos pré e pós crise foram definidas as variáveis “dummy” 𝑍𝑖𝑡, sendo -1 para o período pré-crise (2006-2008) e 1 para o pós-crise (2008-2009), e 𝑍𝑖𝑡𝑡 para verificar se houve diferença na inclinação da reta entre esses períodos, ou seja, se houve mudança na tendência dos indicadores e no deslocamento da reta (intercepto). Para a análise residual foi utilizado os testes de Shapiro-Wilk e Durbin-Watson e análises gráficas, já para verificar a adequabilidade dos modelos foram utilizados a raiz do erro quadrático médio (RMSE), o erro médio absoluto (MAE) e o coeficiente de determinação (𝑅2). Os modelos obtiveram bons resultados de maneira geral, todos apontaram diferença significativa entre o período pré e pós crise, entretanto os resíduos do modelo utilizando harmônicos para o IPCA não passaram no teste de Durbin-Watson e para o Índice de Preços das Importações e Exportações o teste foi inconclusivo. Os modelos utilizando a matriz de delineamento não tiveram problemas com autocorrelação dos resíduos e não tiveram um ajuste muito inferior se comparado aos harmônicos, entretanto apenas a Taxa Juros obteve um parâmetro significativo para a componente sazonal, logo os modelos se reduziram a uma regressão linear múltipla com variáveis ‘dummy’, pois apenas a componente de tendência foi significativa.
The 2008 global financial crisis was the most significant crisis since 1929, impacting various countries worldwide, including Brazil. One way to measure this impact on the economy is through several economic indicators. This study aims to use statistical techniques to model some of these indicators, such as the IPCA (Consumer Price Index), Export and Import Prices, and Interest and Exchange Rates. Monthly values from 2006 to 2009 were collected for the analyses. Regression models, including temporal decomposition and harmonic regression (sinusoidal and cosinusoidal functions), along with dummy variables, were applied. To assess the difference between pre and post-crisis periods, dummy variables 𝑍𝑖𝑡 were defined, with -1 representing the pre-crisis period (2006-2008) and 1 representing the post-crisis period (2008-2009). Additionally, 𝑍𝑖𝑡𝑡 was defined to examine if there was a difference in the slope of the line between these periods, indicating a change in the indicators' trends and intercept displacement. For residual analysis, Shapiro-Wilk and Durbin-Watson tests, along with graphical analyses, were employed. To assess model adequacy, root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (𝑅2) were used. In general, the models yielded good results, indicating a significant difference between the pre and post-crisis periods. However, the residuals of the harmonic model for IPCA did not pass the Durbin-Watson test, and the test for the Import and Export Price Index was inconclusive. The models using the design matrix did not encounter issues with autocorrelation of residuals and did not exhibit a significantly inferior fit compared to the harmonic models. However, only the Interest Rate obtained a significant parameter for the seasonal component. Consequently, the models were simplified to a multiple linear regression with dummy variables, as only the trend component proved to be statistically significant.
The 2008 global financial crisis was the most significant crisis since 1929, impacting various countries worldwide, including Brazil. One way to measure this impact on the economy is through several economic indicators. This study aims to use statistical techniques to model some of these indicators, such as the IPCA (Consumer Price Index), Export and Import Prices, and Interest and Exchange Rates. Monthly values from 2006 to 2009 were collected for the analyses. Regression models, including temporal decomposition and harmonic regression (sinusoidal and cosinusoidal functions), along with dummy variables, were applied. To assess the difference between pre and post-crisis periods, dummy variables 𝑍𝑖𝑡 were defined, with -1 representing the pre-crisis period (2006-2008) and 1 representing the post-crisis period (2008-2009). Additionally, 𝑍𝑖𝑡𝑡 was defined to examine if there was a difference in the slope of the line between these periods, indicating a change in the indicators' trends and intercept displacement. For residual analysis, Shapiro-Wilk and Durbin-Watson tests, along with graphical analyses, were employed. To assess model adequacy, root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (𝑅2) were used. In general, the models yielded good results, indicating a significant difference between the pre and post-crisis periods. However, the residuals of the harmonic model for IPCA did not pass the Durbin-Watson test, and the test for the Import and Export Price Index was inconclusive. The models using the design matrix did not encounter issues with autocorrelation of residuals and did not exhibit a significantly inferior fit compared to the harmonic models. However, only the Interest Rate obtained a significant parameter for the seasonal component. Consequently, the models were simplified to a multiple linear regression with dummy variables, as only the trend component proved to be statistically significant.
Descrição
Palavras-chave
Crise financeira mundial de 2008, Indicadores econômicos, Modelos decomposição de séries temporais, Variáveis dummy, Matriz de delineamento, Harmônicas, Global financial crisis of 2008, Economic indicators, Time series decomposition models, Dummy variables, Design matrix, Harmonics
Como citar
PERON, Roger Arthur Novaes. Modelagem econométrica dos principais indicadores econômicos do Brasil: pré e pós a crise financeira mundial de 2008. Orientador: Manoel Ivanildo Silvestre Bezerra. 2023. 73 f. Trabalho de Conclusão de Curso (Bacharelado em Estatística) - Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista, Presidente Prudente, 2023.